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Cram�r-Rao inequalities for operator-valued measures in quantum mechanics

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/j.1538-7305.1971.tb02544.xopenalex-snapshot
An Image Band Interpretation of Optical Heterodyne Noise
inferredcites →https://doi.org/10.1007/bfb0061483openalex-snapshot
Statistical problems in quantum physics
inferredcites →https://doi.org/10.1016/0375-9601(67)90366-0openalex-snapshot
Minimum mean-squared error of estimates in quantum statistics
inferredcites →https://doi.org/10.1016/c2013-0-02193-7openalex-snapshot
Statistical Theory of Signal Detection
inferredcites →https://doi.org/10.1016/s0019-9958(67)90302-6openalex-snapshot
Detection theory and quantum mechanics
inferredcites →https://doi.org/10.1063/1.1665962openalex-snapshot
Operator Valued Measures in Quantum Mechanics: Finite and Infinite Processes
inferredcites →https://doi.org/10.1063/1.1666075openalex-snapshot
Decision Procedures in Quantum Mechanics
inferredcites →https://doi.org/10.1063/1.3022201openalex-snapshot
Statistical Theory Of Signal Detection
inferredcites →https://doi.org/10.1103/physrev.131.2766openalex-snapshot
Coherent and Incoherent States of the Radiation Field
inferredcites →https://doi.org/10.1103/physrev.152.1103openalex-snapshot
Simultaneous Measurement of Noncommuting Observables
inferredcites →https://doi.org/10.1109/tit.1968.1054108openalex-snapshot
The minimum variance of estimates in quantum signal detection
inferredcites →https://doi.org/10.1109/tit.1971.1054643openalex-snapshot
Application of quantum estimation theory to analog communication over quantum channels
inferredcites →https://doi.org/10.1109/tit.1974.1055173openalex-snapshot
Noncommuting observables in quantum detection and estimation theory
inferredcites →https://doi.org/10.1214/aoms/1177732144openalex-snapshot
Contributions to the Theory of Statistical Estimation and Testing Hypotheses
inferredcites →https://doi.org/10.1515/9783112706152openalex-snapshot
Theorie der linearen Operatoren im Hilbert-Raum
inferredcites →https://doi.org/10.1515/9783112708057openalex-snapshot
Theorie der linearen Operatoren im Hilbert-Raum
inferredcites →https://doi.org/10.2307/2226151openalex-snapshot
Mathematical Methods of Statistics.
inferredcites →https://doi.org/10.2307/2342525openalex-snapshot
Theory of Games and Statistical Decisions.
inferredcites →https://doi.org/10.2307/3497265openalex-snapshot
Theory of Games and Statistical Decisions

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Quantum‐Mechanical System Theory: a Unifying Framework for Observations and Stochastic Processes in Quantum Mechanics
inferred← citeshttps://doi.org/10.1007/bf00666052openalex-snapshot
Simultaneous SO(2n) generator measurement by spin-clifford algebra coupling
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Relativistic field formulation of simultaneous quantum measurement
inferred← citeshttps://doi.org/10.1007/bf00708521openalex-snapshot
?Simultaneous measurement? from the standpoint of quantum estimation theory
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On the simultaneous measurement of position and momentum: Naimark embeddings and projections
inferred← citeshttps://doi.org/10.1007/bf00734524openalex-snapshot
On the simultaneous measurement of spin components using spin-1/2 meters: Naimark embedding and projections
inferred← citeshttps://doi.org/10.1007/bf01032091openalex-snapshot
Generalized uncertainty relations and efficient measurements in quantum systems
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An optimization problem from linear filtering with quantum measurements
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Optimum measurements for discrimination among symmetric quantum states and parameter estimation
inferred← citeshttps://doi.org/10.1007/bf02743060openalex-snapshot
Quantum and other physics as systems theory
inferred← citeshttps://doi.org/10.1007/s10773-019-04174-9openalex-snapshot
Quantum Sensing of Curvature
inferred← citeshttps://doi.org/10.1007/s43673-023-00089-0openalex-snapshot
Enhanced parameter estimation by measurement of non-Hermitian operators
inferred← citeshttps://doi.org/10.1016/0020-0255(75)90016-xopenalex-snapshot
Asymptotically efficient approaches to quantum-mechanical parameter estimation
inferred← citeshttps://doi.org/10.1016/s0076-5392(08)60260-xopenalex-snapshot
References
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Toward incompatible quantum limits on multiparameter estimation
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QUANTUM OPTIMALITY OF PHOTON COUNTING FOR TEMPERATURE MEASUREMENT OF THERMAL ASTRONOMICAL SOURCES
inferred← citeshttps://doi.org/10.1088/1367-2630/ac1186openalex-snapshot
RLD Fisher information bound for multiparameter estimation of quantum channels
inferred← citeshttps://doi.org/10.1103/389g-d3syopenalex-snapshot
Heisenberg-limited two-parameter estimation with weighted three-mode Schrödinger cat states in a triple-well Bose-Einstein condensate system
inferred← citeshttps://doi.org/10.1103/physreva.100.032126openalex-snapshot
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Ultimate limits of thermal pattern recognition
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Quantum-enhanced passive remote sensing
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inferred← citeshttps://doi.org/10.1103/physreva.38.3556openalex-snapshot
Quantum correlation and state reduction of photon twins produced by a parametric amplifier
inferred← citeshttps://doi.org/10.1103/physreva.50.3682openalex-snapshot
Fundamental limits upon the measurement of state vectors
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Canonical Naimark extension for generalized measurements involving sets of Pauli quantum observables chosen at random
inferred← citeshttps://doi.org/10.1103/physreva.97.062302openalex-snapshot
Analysis of quantum information processors using quantum metrology
inferred← citeshttps://doi.org/10.1103/physrevlett.123.143604openalex-snapshot
Optimal Imaging of Remote Bodies Using Quantum Detectors
inferred← citeshttps://doi.org/10.1103/physrevlett.126.120503openalex-snapshot
Incorporating Heisenberg’s Uncertainty Principle into Quantum Multiparameter Estimation
inferred← citeshttps://doi.org/10.1103/physrevresearch.2.023038openalex-snapshot
Quantum theory of polarimetry: From quantum operations to Mueller matrices
inferred← citeshttps://doi.org/10.1103/physrevresearch.3.033079openalex-snapshot
Canonical quantization on the half-line and in an interval based upon an alternative concept for the momentum in a space with boundaries
inferred← citeshttps://doi.org/10.1109/tit.1977.1055794openalex-snapshot
Quantum mechanical linear filtering of vector signal processes
inferred← citeshttps://doi.org/10.1111/1467-9868.00415openalex-snapshot
On Quantum Statistical Inference
inferred← citeshttps://doi.org/10.1111/1467-9868.00416openalex-snapshot
Discussion on the Paper by Barndorff-Nielsen, Gill and Jupp
inferred← citeshttps://doi.org/10.1116/1.5119961openalex-snapshot
Geometric perspective on quantum parameter estimation
inferred← citeshttps://doi.org/10.1126/sciadv.adm8524openalex-snapshot
Nanoradian-scale precision in light rotation measurement via indefinite quantum dynamics
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Logarithmic derivative operators, Cramér–Rao bounds, and Fisher information in quantum information theory
inferred← citeshttps://doi.org/10.1142/s0219749914610127openalex-snapshot
Probing qubit by qubit: Properties of the POVM and the information/disturbance tradeoff
inferred← citeshttps://doi.org/10.1142/s0219749917500290openalex-snapshot
An effective iterative method to build the Naimark extension of rank-n POVMs
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Report on scipost_202306_00025v1
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Report on scipost_202306_00025v3
inferred← citeshttps://doi.org/10.21468/scipostphys.16.1.013openalex-snapshot
Optimal control strategies for parameter estimation of quantum systems
inferred← citeshttps://doi.org/10.48350/162001openalex-snapshot
Canonical quantization on the half-line and in an interval based upon an alternative concept for the momentum in a space with boundaries
inferred← citeshttps://doi.org/10.70675/6a4ca4b4z7223z45d3z8adfz6302e3e55033openalex-snapshot
Description and Control of systems for quantum technologies : from nuclear spins to cold atoms
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